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FABLE. THE ORIGINS OF NUMERATION AND ARITHMETIC. Pamela Leutwyler. Once upon a time, in ancient Greece, there was a USED CAMEL DEALER. Each day, he counted his camels. This was difficult. They would not stand still. They all looked alike. And sometimes…. It was cold and rainy.

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FABLE

THE ORIGINS OF NUMERATION

AND ARITHMETIC

Pamela Leutwyler



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Each day, he counted his camels.

This was difficult. They would not stand still.

They all looked alike. And sometimes…



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So one day, the used camel dealer got a good idea.

Having just counted, he knew exactly

How many camels were on the lot.

used camels

He went into his showroom


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Where he built a shallow box on the floor

In which he placed ONE pebble to

represent each camel on his lot.


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If 2 camels are born

If he bought 2 camels

If 1 camel dies

If he sold 3 camels


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This system was an improvement over running around in all kinds

Of weather to chase and count the actual camels. But as he

Prospered, the huge pile of pebbles became awkward to count.


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This system was an improvement over running around in all kinds

Of weather to chase and count the actual camels. But as he

Prospered, the huge pile of pebbles became awkward to count.

Then he got a really good idea!


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The pebbles are temporarily removed kinds

Then partitions are built

The first pile will function just as the original pebble board

One pebble

represents one camel


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In this pile 1 pebble represents 1 camel kinds

Let’s view the pebble board from the top

3 camels are born

1 camel dies

he sells 1 camel

he buys 5 camels


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Instead of allowing the pebbles to pile up, the dealer makes this rule:

In this pile 1 pebble represents 1 camel

When 10 pebbles accumulate in a pile, they are replaced with

1 pebble in the next pile


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Instead of allowing the pebbles to pile up, the dealer makes this rule:

In this pile 1 pebble represents 10 camels

When 10 pebbles accumulate in a pile, they are replaced with

1 pebble in the next pile


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Instead of allowing the pebbles to pile up, the dealer makes this rule:

When 10 pebbles accumulate in a pile, they are replaced with

1 pebble in the next pile

Ten tens become

1 hundred


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How many camels? this rule:


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This is beginning to look familiar. Representing a camel with a

Pebble was the first level of abstraction. Next, piles of pebbles will

Be replaced with symbols. Then, we do not need pebbles and boards.

5

2

3


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The laws of arithmetic with a

arise from this pebble board


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6 with a

5

+

4

8


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3 with a

Put down 3

6

5

+

4

8


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3 with a

1

Put down 3

6

5

Carry 1

+

4

8


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1 with a

3

1

1

Put down 3

6

5

Carry 1

+

4

8

Put down 1

1

Carry 1


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2 with a

5

-

8


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1 with a

Borrow 1

1

2

5

-

8


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1 with a

Borrow 1

1

2

5

-

8

1 7


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Why did the used camel dealer choose the number with a10 ?

Probably it was because he had 10 fingers.

Our numeration system is called base ten.

If we choose another number – lets say 7 - when we

Make the rule about when to move pebbles, we generate a

BASE SEVEN NUMERATION SYSTEM


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